Device

Software

TI-Nspire Version

Objectives

Visualize the solid generated by revolving the region bounded between two function graphs and the vertical lines x = a and x = b about the x-axis

Calculate the area of a cross section of a solid generated by rotating the region bounded between two function graphs and the vertical lines x = a and x = b about the x-axis

Use the area of a cross section of a solid generated by rotating a region bounded by two function graphs about the x-axis to find the exact volume of the solid

Vocabulary

revolve about the x-axis

solid

washer

About the Lesson

The intent of this lesson is to provide students with visual representations of solids of revolution. As a result, students will:

Observe that the solid generated by revolving the region bounded between two functions about the x-axis has cross sections shaped like washers centered on the x-axis, the radii of which correspond to the values of the upper function and the lower function at that point.

Observe that the volume of a solid of revolution can be estimated using a sum of volumes of washer slices.